The victims died when a strike from an aircraft hit a house in the Shigal district of Kunar province during an operation which also killed at least eight militants.

The Nato-led coalition confirmed it was investigating the allegation and that it had used aircraft in the area to support a force of Afghan and foreign troops.

The incident had the potential to provoke another confrontation with Hamid Karzai's government. Mr Karzai has railed for years against the number of civilian casualties caused by Nato air strikes, though deaths from such air attacks have decreased significantly. The setback came as Gen Martin Dempsey, the chairman of the US military's joint chiefs, declared that the conflict would last another decade, persisting far beyond the American-led withdrawal of foreign forces next year.

He was asked if he thought that conflict would still be raging in Afghanistan even though Nato forces have pulled out. He said: "Yes, of course there will be. And if we were having this conversation 10 years from now, I suspect there would [still] be contested areas because the history of Afghanistan suggests that there will always be contested areas."

Haji Mia Hassan, chief of the Kunar provincial council, said that a delegation from the area was being assembled to investigate and if necessary petition Mr Karzai for justice.

He said: "We heard this morning and the people are not happy. Eleven children were killed and one woman and eight Taliban. People say that the Americans said they wanted to help the Afghans and now they are killing them."

The fighting in Kunar on Saturday also led to the death of a US civilian adviser. An Afghan security official in the area said the joint operation had been launched after intelligence reports showed that hundreds of Taliban militants were massing in the area. Kunar, on the mountainous and often heavily forested border with Pakistan, has been notorious for harbouring a complex mix of insurgent factions.

At one point during the operation, the government force was surrounded in a village and Nato forces called for air support. The picture was clouded by the possibility that an insurgent had detonated a suicide vest, the official said.

The dead militants included Ali Khan and Gul Raouf, commanders who planned and organised attacks in Kunar, according to the Afghan interior ministry.

A spokesman for the coalition said: "We take all reports of civilian casualties seriously."

The fighting took place on the same day that three American soldiers and two US civilians died in a suicide car bomb attack in Zabul province, southern Afghanistan. One of those who died was a young American foreign service officer who became the first US diplomat to die in the line of duty since last September's attack on the embassy in Benghazi, Libya.

Anne Smedinghoff, 25, died as her convoy was hit on its way to distribute books to a school in Zabul. John Kerry, the US secretary of state, paid tribute to her during a visit to Istanbul.

He said he had known her personally because she had acted as an aide when he visited Kabul earlier in the year.

He described her as "vivacious, smart, capable, chosen often by the ambassador there to be the lead person because of her capacity".

He said: "It's a grim reminder to all of us e_SLpse_STnSof how important, but also how risky, carrying the future is. Folks who want to kill people, and that's all they want to do, are scared of knowledge."